Nader Masmoudi

Masmoudi is particularly concerned with nonlinear partial differential equations of hydrodynamics (Euler equation, Navier-Stokes equation, surface waves, gravity waves, capillary waves, acoustic waves, boundary layer equations and qualitative behavior of boundary layers, Couette flow, non-Newtonian fluids, nonlinear Schrödinger equations for waves and others dispersive systems, etc.), hydrodynamic limit value of the Boltzmann equation, limit behavior to incompressibility, chemotaxis (Keller-Segel equations), the Ginsburg-Landau equation, Landau damping, behavior of mixtures, general long-term behavior of semilinear systems of partial differential equations and stability problems in hydrodynamics . In 2013, together with his post-doctoral student Jacob Bedrossian, he strictly demonstrated the stability of the shear flow according to Couette for the two-dimensional Euler equations, i.e. in the non-linear case. The stability in linear approximation was already proven by Lord Kelvin in 1887 and more precisely by William McFadden Orr in 1907. He also obtained similar stability results in the viscous case for the boundary layer formation according to Prandtl in the two-dimensional Navier-Stokes equations (the linear theory is named here after Orr and Arnold Sommerfeld: Orr-Sommerfeld equations). He built on the work on a similar problem by Cédric Villani, who dealt with Landau damping, the damping of plasma waves, which in a strictly mathematical treatment also results from non-viscous phenomena (strong smoothness properties and mixing, sometimes non-viscous damping called (inviscid damping), technically so-called Gevrey regularity) resulted. Possible instabilities also result from non-linear resonances between different waves in the plasma (non-linear build-up with the “echoes” of the waves) and must be “mathematically controlled” in order to prove stability. The behavior of plasmas and non-viscous liquids described by the Euler equation is similar.

He studied in Tunis and then at the École normal supérieure in Paris with a diploma in 1996; In 1999 he received his doctorate from the University of Paris-Dauphine with Pierre-Louis Lions (Problemes asymptotiques en mecanique des fluides). He then went to the Courant Institute at New York University, where he became a professor in 2008.

In 1992 he received a gold medal at the International Mathematical Olympiad (as the first African or Arab at all). For 2017 he received the Fermat Prize. In 2018 he was invited speaker at the International Congress of Mathematicians in Rio de Janeiro. In 2021 Masmoudi was elected to the American Academy of Arts and Sciences. In 2022 he was awarded the International King Faisal Prize jointly with Martin Hairer.

Nader Masmoudi (born 1974 in Sfax) is a Tunisian mathematician.